Finite Group Databasebeta

← Prev (#36381110) Next (#36381112) →

H(3,𝔽₃)×C₃₁⋊C₂₇ #36381111

order	22599
automorphism	?
homology	Abelianization (H₁) = C₃²×C₂₇ · Schur multiplier (H₂) = C₃⁴

Aliases

H(3,𝔽₃)×C₃₁⋊C₂₇

Splittings

C₃₁ ⋊ C₂₇×H(3,𝔽₃)

Subgroups

	subgroup	G/H
center, Frattini	C₃×C₉	C₃²×C₃₁⋊C₃
commutator	C₃×C₃₁	C₃²×C₂₇
Fitting	C₉×H(3,𝔽₃)×C₃₁	C₃
socle	C₃²×C₃₁	C₃²×C₉
prime radical	C₃×H(3,𝔽₃)×C₃₁	C₉
cosocle	C₃×C₉×C₃₁	C₃³
hypercenter	C₉×H(3,𝔽₃)	C₃₁⋊C₃
hypocenter	C₃₁	C₂₇×H(3,𝔽₃)
LCS	G ▷ C₃×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₃×C₉ ◁ C₉×H(3,𝔽₃)

292 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 7533

Conjugacy classes & character table

1287 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22599, 2132);